SOLUTION: use each function to find f(g(x) and g(f(x)) f(x)=|x| , g(x)=5x+1

f(g(x))

means to substitute the right side of g(x) for x in the right side of f(x).

So we take the right side of f(x) which is |x| and substitute the right side
of g(x), which is (5x+1) for x in |x| getting |5x+1|.

so 

f(g(x)) = |5x+1|

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g(f(x))

means to substitute the right side of f(x) for x in the right side of g(x).

So we take the right side of g(x) which is 5x+1 and substitute the right side
of f(x), which is |x| for x in 5x+1 getting 5|x|+1.

so 

g(f(x)) = 5|x|+1

Edwin